Irrigation Water Conveyance and Application Methods
Subtopic: Design of irrigation channels and underground pipelines
Question Statement:
The most economical trapezoidal channel section with 1:1 (horizontal:vertical) side slope is designed to carry a maximum of 40 cm depth of water at its full capacity. If the bed slope of the channel is 1:2500 and the Manning's roughness coefficient of channel section is 0.01, the estimated discharge capacity of the channel in m³·s⁻¹ is ______. [round off to 2 decimal places]
Official Answer Key:
0.18 to 0.22
Step-by-Step Solution & Explanation
For the most economical trapezoidal section with side slope z=1, bed width b = 2d(√(1+z²) − z) = 2×0.4×(√2 −1) = 0.8×0.4142 = 0.331 m, and hydraulic radius R = d/2 = 0.20 m. Area A = (b + z·d)·d = (0.331+0.40)×0.40 = 0.2926 m². Manning's equation: V = (1/n)R^(2/3)S^(1/2) = (1/0.01)×0.20^(0.667)×(1/2500)^0.5 = 100×0.342×0.02 = 0.684 m/s. Discharge Q = A×V = 0.2926×0.684 = 0.20 m³/s.
Practice This in Real CBT Exam Interface
Test yourself with the official TCS-iON palette, virtual calculator, and immediate performance analytics.